Hi! as suggested by @Emil_G you should first post the status of your actual flash areas by using show version and show flash commands.
Also a verify signature flash primary (and/or secondary) would be of help to undestand the status of flashed firmware on primary (and/or secondary) flash area.
Genearlly a straight procedure would be (never had an issue downloading a SWI file from a well connected and reacheable TFTP Server):
switch# show version
Image stamp: /ws/swbuildm/rel_ajanta_qaoff/code/build/lakes(swbuildm_rel_ajanta_qaoff_rel_ajanta)
Jan 17 2020 05:48:13
YA.16.10.0003
391
Boot Image: Secondary
Boot ROM Version: YA.15.20
switch# show flash
Image Size (bytes) Date Version
----------------- ------------ -------- --------------
Primary Image : 15069009 01/17/20 YA.16.10.0003
Secondary Image : 15069009 01/17/20 YA.16.10.0003
Boot ROM Version
----------------
Primary Boot ROM Version : YA.15.20
Default Boot Image : Secondary
switch# verify signature flash primary
Signature is valid
switch# verify signature flash secondary
Signature is valid
switch# copy tftp flash <TFTP-Server-IP-Address> YA_16_10_0007.swi primary
The primary image will be deleted.
Continue (y/n)? y
015M
Validating and Writing System Software to the Filesystem ...
switch# show flash
Image Size (bytes) Date Version
----------------- ------------ -------- --------------
Primary Image : 15100980 04/17/20 YA.16.10.0007
Secondary Image : 15069009 01/17/20 YA.16.10.0003
Boot ROM Version
----------------
Primary Boot ROM Version : YA.15.20
Default Boot Image : Secondary
switch# verify signature flash primary
Signature is valid
switch# boot system flash primary
The switch will reboot
switch# show version
Image stamp: /ws/swbuildm/ajanta_qt_qaoff/code/build/lakes(swbuildm_ajanta_qt_qaoff_ajanta_qt)
Apr 17 2020 04:27:04
YA.16.10.0007
240
Boot Image: Primary
Boot ROM Version: YA.15.20
switch# show flash
Image Size (bytes) Date Version
----------------- ------------ -------- --------------
Primary Image : 15100980 04/17/20 YA.16.10.0007
Secondary Image : 15069009 01/17/20 YA.16.10.0003
Boot ROM Version
----------------
Primary Boot ROM Version : YA.15.20
Default Boot Image : Primary
switch# copy flash flash secondary
switch# show flash
Image Size (bytes) Date Version
----------------- ------------ -------- --------------
Primary Image : 15100980 04/17/20 YA.16.10.0007
Secondary Image : 15100980 04/17/20 YA.16.10.0007
Boot ROM Version
----------------
Primary Boot ROM Version : YA.15.20
Default Boot Image : Primary
In the example above an Aruba 2530 with a recent YA.16.10.0003 (booted on Primary) is updated to YA.16.10.0007 (latest, released just few days ago).
I upload from TFTP Server the firmware YA_16_10_0007.swi on the Secondary flash area. Then I set the next boot to start from Secondary instead of (default) Primary. That's it. Apart from verifying the flashed firmwares (current and the updated ones) in the end, if no issue will arise, I tend to copy the updated flashed area on the other (non updated) in order to have both areas equally updated.
The update procedure of an Aruba (HP) 2920, if made with the help of a TFTP Server, is identical.